There are 12 balloons in a bag: 3 each of blue, green, red, and yellow. Three balloons are chosen at random. Find the probability that all 3 of the balloons are green,
Thank you so much for the help.
To start out, what is the probability that the first balloon is green?
1/4
Yes, that's correct. What is the probability that the second balloon is also green?
I think 2/11 but I am not sure 🤔
also correct
And then 1/10
Yep, so then you can just multiply your three probabilities together, since they all need to be true to satisfy your original condition of three green balloons, and then you have your answer.
Nice going on this, btw.
Thank you so much.
To find the probability that all three balloons chosen are green, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Out of the 12 balloons, we are choosing 3, which can be represented as "12 choose 3" or C(12, 3). This can be calculated as follows:
C(12, 3) = 12! / (3! (12 - 3)!)
= 12! / (3! 9!)
= (12 * 11 * 10) / (3 * 2 * 1)
= 220
So, there are 220 possible outcomes when choosing 3 balloons out of 12.
Number of favorable outcomes:
Since there are 3 green balloons in the bag, we need to choose all 3 of them. This can be represented as "3 choose 3" or C(3, 3), which is equal to 1.
So, there is only 1 favorable outcome where all 3 balloons chosen are green.
Therefore, the probability that all 3 of the balloons chosen are green is:
P(3 green balloons) = number of favorable outcomes / total number of possible outcomes
= 1 / 220
Hence, the probability is 1/220.
You're welcome! Let me know if there is anything else I can help you with.